Stratospheric sudden warmings as self-tuning resonances

The fundamental dynamics of `vortex splitting' stratospheric sudden warmings (SSWs), which are known to be predominantly barotropic in nature, are re-examined using an idealized single layer f-plane model of the polar vortex. The aim is to elucidate the conditions under which a stationary topographic forcing causes the model vortex to split, and to express the splitting condition as a function of the model parameters determining the topography and circulation. For a specified topographic forcing profile the model behavior is governed by two nondimensional parameters; the topographic forcing height M and a surf-zone potential vorticity parameter Ω. For relatively low M, vortex splits similar to observed SSWs occur only for a narrow range of Ω values. Further, a bifurcation in parameter space is observed: a small change in Ω (or M) beyond a critical value can lead to an abrupt transition between a state with low amplitude vortex Rossby waves and a sudden vortex split. The model behavior can be fully understood using two nonlinear analytical reductions: the Kida model of elliptical vortex motion in a uniform strain flow, and a forced nonlinear oscillator equation. The abrupt transition in behavior is a feature of both reductions, and corresponds to the onset of a nonlinear (self-tuning) resonance. The extent to which the above ideas apply to vortex displacement SSWs, for which the relevant mode has a baroclinic structure, is examined briefly using three-dimensional calculations. Nonlinearity in the vortex displacement case is found to be more complicated, involving some wave breaking in the upper part of the vortex regardless of whether resonance is attained. Nevertheless the same general picture appears to hold, and an example of an `SSW' observed in the numerical experiments is shown in the figure. The results add an important new aspect to the `resonant excitation' theory of SSWs. Under this paradigm, it is not necessary to invoke an anomalous tropospheric planetary wave source, or unusually favorable conditions for upward wave propagation, in order to explain the occurrence of SSWs. Refs: Matthewman and Esler, 2011, J. Atmos. Sci., 68, 2481–2504; Esler and Matthewman, 2011, J. Atmos. Sci., 68, 2505–2523.